Bayesian Cluster Geographically Weighted Regression for Spatial Heterogeneous Data

Abstract: Spatial statistical models are commonly used in geographical scenarios to ensure spatial variation is captured effectively. However, spatial models and cluster algorithms can be complicated and expensive. This paper pursues three main objectives. First, it introduces covariate effect clustering by integrating a Bayesian Geographically Weighted Regression (BGWR) with a Gaussian mixture model and the Dirichlet process mixture model. Second, this paper examines situations in which a particular covariate holds significant importance in one region but not in another in the Bayesian framework. Lastly, it addresses computational challenges present in existing BGWR, leading to notable enhancements in Markov chain Monte Carlo estimation suitable for large spatial datasets. The efficacy of the proposed method is demonstrated using simulated data and is further validated in a case study examining children's development domains in Queensland, Australia, using data provided by Children's Health Queensland and Australia's Early Development Census.